That's somewhat narrowly defined considering they're really the only remaining producer of mainframes. I'm not sure if that's literally true but it may as well be.

There are some things that mainframes are legitimately better at, and some things that POWER is better at than x86, and so on. AMD and Intel benefit from incredible economies of scale that IBM could never dream of, and that's mostly where IBM loses -- the price is a lot higher and the volume a lot lower on the IBM side.

I thought HP still had some weight to throw around the mainframe arena? Or has that changed by now?

And Cray still exists.

But are mainframes themselves the cutting edge of modern computing?

Well, some consider "cloud" to be a sort of mainframe revival, so in that sense, maybe? But not in the "room-sized computer" sense, no.